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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.powers.hypot"></a><a class="link" href="hypot.html" title="hypot">hypot</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>
</pre>
<p>
        <span class="bold"><strong>Effects: </strong></span> computes
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>

        </p></blockquote></div>
<p>
        in such a way as to avoid undue underflow and overflow.
      </p>
<p>
        The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
        type calculation rules</em></span></a> when T1 and T2 are of different
        types.
      </p>
<p>
        The final <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
        be used to control the behaviour of the function: how it handles errors,
        what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">policy
        documentation for more details</a>.
      </p>
<p>
        When calculating
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hypot.svg"></span>

        </p></blockquote></div>
<p>
        it's quite easy for the intermediate terms to either overflow or underflow,
        even though the result is in fact perfectly representable.
      </p>
<h5>
<a name="math_toolkit.powers.hypot.h0"></a>
        <span class="phrase"><a name="math_toolkit.powers.hypot.implementation"></a></span><a class="link" href="hypot.html#math_toolkit.powers.hypot.implementation">Implementation</a>
      </h5>
<p>
        The function is even and symmetric in <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>,
        so first take assume <span class="emphasis"><em>x,y &gt; 0</em></span> and <span class="emphasis"><em>x &gt;
        y</em></span> (we can permute the arguments if this is not the case).
      </p>
<p>
        Then if <span class="emphasis"><em>x * ε &gt;= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
      </p>
<p>
        Otherwise the result is given by:
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/hypot2.svg"></span>

        </p></blockquote></div>
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